{"title":"Conway Numbers – Formal Introduction","authors":"Karol Pąk","doi":"10.2478/forma-2023-0018","DOIUrl":null,"url":null,"abstract":"Summary Surreal numbers, a fascinating mathematical concept introduced by John Conway, have attracted considerable interest due to their unique properties. In this article, we formalize the basic concept of surreal numbers close to the original Conway’s convention in the field of combinatorial game theory. We define surreal numbers with the pre-order in the Mizar system which satisfy the following condition: x ⩽ y iff Lx ≪ {y} Λ {x} ≪ Ry.","PeriodicalId":42667,"journal":{"name":"Formalized Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Formalized Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/forma-2023-0018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Summary Surreal numbers, a fascinating mathematical concept introduced by John Conway, have attracted considerable interest due to their unique properties. In this article, we formalize the basic concept of surreal numbers close to the original Conway’s convention in the field of combinatorial game theory. We define surreal numbers with the pre-order in the Mizar system which satisfy the following condition: x ⩽ y iff Lx ≪ {y} Λ {x} ≪ Ry.
期刊介绍:
Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.